The recent sequencing of the human genome [l, 2] provides a unique opportunity to change the way we understand common human diseases, and ultimately improve diagnosis, prognosis, and treatment of disease [3]. Complex genetic mechanisms that contribute to common diseases pose a significant challenge that must be met with novel analytic methods based on a sound theoretical foundation of biological and statistical principles. The potential benefits of our proposed research are great when measured in terms of public health, with anticipated improvements in the way that genetic mechanisms are discovered and evaluated for common complex human diseases. Our overall objectives are to facilitate analyses of complex genetic mechanisms by developing innovative statistical methods and software that can be used by biomedical researchers as outlined in our four specific aims: Aim 1. Develop and evaluate probability models for haplotypes in order to improve our understanding of the complex structure of haplotypes in human populations and provide methods to account for ambiguous haplotypes when they are not directly observed due to unknown phase of diploid phenotypes. Aim 2. Haplotypes and other complex genetic mechanisms for case- control studies: Build statistical genetic models to evaluate the relative contribution of complex genetic mechanisms (haplotypes and metabolic pathways) and environmental risk factors to disease, as evaluated by standard case-control study designs. Aim 3. Haplotypes and other complex genetic mechanisms for family- based studies: The methods developed in Aims 1 & 2 will be extended to family-based study designs, including a hybrid design that combines the strengths of case-control and family-based designs, increasing power to detect genes of small effects. Aim 4. Develop user-friendly software that implements our methods and make them widely available to biomedical researchers, including well-documented procedures and examples on their usage.